Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics
We study dynamics and thermodynamics of ion transport in narrow, water-filled channels, considered as effective 1D Coulomb systems. The long range nature of the inter-ion interactions comes about due to the dielectric constants mismatch between the water and the surrounding medium, confining the ele...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-01-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/1/125 |
| _version_ | 1797409853490069504 |
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| author | Tobias Gulden Alex Kamenev |
| author_facet | Tobias Gulden Alex Kamenev |
| author_sort | Tobias Gulden |
| collection | DOAJ |
| description | We study dynamics and thermodynamics of ion transport in narrow, water-filled channels, considered as effective 1D Coulomb systems. The long range nature of the inter-ion interactions comes about due to the dielectric constants mismatch between the water and the surrounding medium, confining the electric filed to stay mostly within the water-filled channel. Statistical mechanics of such Coulomb systems is dominated by entropic effects which may be accurately accounted for by mapping onto an effective quantum mechanics. In presence of multivalent ions the corresponding quantum mechanics appears to be non-Hermitian. In this review we discuss a framework for semiclassical calculations for the effective non-Hermitian Hamiltonians. Non-Hermiticity elevates WKB action integrals from the real line to closed cycles on a complex Riemann surfaces where direct calculations are not attainable. We circumvent this issue by applying tools from algebraic topology, such as the Picard-Fuchs equation. We discuss how its solutions relate to the thermodynamics and correlation functions of multivalent solutions within narrow, water-filled channels. |
| first_indexed | 2024-03-09T04:21:34Z |
| format | Article |
| id | doaj.art-0821ff002ca741e2912deec288310ddc |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T04:21:34Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-0821ff002ca741e2912deec288310ddc2023-12-03T13:46:14ZengMDPI AGEntropy1099-43002021-01-0123112510.3390/e23010125Dynamics of Ion Channels via Non-Hermitian Quantum MechanicsTobias Gulden0Alex Kamenev1Institute of Science and Technology Austria, 3400 Klosterneuburg, AustriaSchool of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USAWe study dynamics and thermodynamics of ion transport in narrow, water-filled channels, considered as effective 1D Coulomb systems. The long range nature of the inter-ion interactions comes about due to the dielectric constants mismatch between the water and the surrounding medium, confining the electric filed to stay mostly within the water-filled channel. Statistical mechanics of such Coulomb systems is dominated by entropic effects which may be accurately accounted for by mapping onto an effective quantum mechanics. In presence of multivalent ions the corresponding quantum mechanics appears to be non-Hermitian. In this review we discuss a framework for semiclassical calculations for the effective non-Hermitian Hamiltonians. Non-Hermiticity elevates WKB action integrals from the real line to closed cycles on a complex Riemann surfaces where direct calculations are not attainable. We circumvent this issue by applying tools from algebraic topology, such as the Picard-Fuchs equation. We discuss how its solutions relate to the thermodynamics and correlation functions of multivalent solutions within narrow, water-filled channels.https://www.mdpi.com/1099-4300/23/1/125non-Hermitian Hamiltoniansalgebraic topologysemiclassical methodsnanoporesion transportstatistical mechanics |
| spellingShingle | Tobias Gulden Alex Kamenev Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics Entropy non-Hermitian Hamiltonians algebraic topology semiclassical methods nanopores ion transport statistical mechanics |
| title | Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics |
| title_full | Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics |
| title_fullStr | Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics |
| title_full_unstemmed | Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics |
| title_short | Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics |
| title_sort | dynamics of ion channels via non hermitian quantum mechanics |
| topic | non-Hermitian Hamiltonians algebraic topology semiclassical methods nanopores ion transport statistical mechanics |
| url | https://www.mdpi.com/1099-4300/23/1/125 |
| work_keys_str_mv | AT tobiasgulden dynamicsofionchannelsvianonhermitianquantummechanics AT alexkamenev dynamicsofionchannelsvianonhermitianquantummechanics |